Kirk played domestic rugby for Otago and Auckland, and first toured with the All Blacks in 1983. He stood out from his fellow players as "urbane, articulate and thoughtful,"[2] and when the planned 1986 All Black tour to South Africa was cancelled David and John Kirwan were the only two players to refuse to join the rebel "Cavaliers" team on moral grounds—he felt that it would give comfort to the apartheid regime.

With the rebels banned from playing in the next two All Black test he captained the so-called "Baby Blacks". On the return of the rebels however, his position was uncomfortable and he was lucky to retain his place in the squad. Despite this, when original captain Andy Dalton had to withdraw with an injury,[3] Kirk was made captain—and led New Zealand to victory over France in the 1987 Rugby World Cup Final.

His most recent involvement with rugby came in late 2009, when he led an independent arbitration panel appointed by SANZAR to settle an impasse between its three member unions (South Africa, New Zealand and Australia) over whether the planned 15th franchise in the Super Rugby competition would be awarded to Australia or South Africa, Ultimately, Melbourne was chosen and began play in 2011.

On 24 October 2011, Kirk was inducted into the IRB Hall of Fame alongside all other Rugby World Cup-winning captains and head coaches from the tournament's inception in 1987 through to 2007 (minus the previously inducted John Eales).[7]